question B needs more explaination
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question B needs more explaination Challenge Problem: Suppose that we toss a biased coin repeatedly with...
9.74. Suppose we toss a biased coin independently until we get two heads or two tails in total. The coin produces a head with probability p on any toss. 1. What is the sample space of this experiment? 2. What is the probability function? 3. What is the probability that the experiment stops with two heads?
2. SUPPLEMENTAL QUESTION 1 (a) Toss a fair coin so that with probability pheads occurs and with probability p tails occurs. Let X be the number of heads and Y be the number of tails. Prove X and Y are dependent (b) Now, toss the same coin n times, where n is a random integer with Poisson distribution: n~Poisson(A) Let X be the random variable counting the number of heads, Y the random variable counting the number of tails. Prove...
Problem 7. Suppose that a coin will be tossed repeatedly 100 times; let N be the number of Heads obtained from 100 fips of this coin. But you are not certain that the coin is a fair coin.it might be somewhat biased. That is, the probability of Heads from a single toss might not be 1/2. You decide, based on prior data, to model your uncertainty about the probability of Heads by making this probability into random variable as wl....
Please explain the reasoning with calculation, thank you! Question: If we toss a coin n times. x and y are number of heads and tails. What's the correlation coeffcient between x and y? a)-1 b)0 c)1/2 d)1
Suppose we toss a coin (with P(H) p and P(T) 1-p-q) infinitely many times. Let Yi be the waiting time for the first head so (i-n)- (the first head occurs on the n-th toss) and Xn be the number of heads after n-tosses so (X·= k)-(there are k heads after n tosses of the coin). (a) Compute the P(Y> n) (b) Prove using the formula P(AnB) P(B) (c) What is the physical meaning of the formula you just proved? Suppose...
2. Suppose we want to test whether a coin is fair (that is, the probability of heads is p = .5). We toss the coin 1000 times, and record the number of heads. Let T denote the number of heads divided by 1000. Consider a test that rejects the null hypothesis that p=.5 if T > c. (a) Write down a formula for P(T>c) assuming p = 0.5. (This formula may be compli- cated, but try to give an explicit...
We toss a fair coin n 400 times and denote Zn the number of heads. (a) What are E(Zn) et Var(Zn)1? (b) What is the probability that Z 200? (use the normal approximation together with the continuity correction (c) What is the smallest integer m such that Pr 200-mくZ.く200 +m] > 20%? (use the normal approximation together with the continuity correction). We toss a fair coin n 400 times and denote Zn the number of heads. (a) What are E(Zn)...
Question 2 Suppose you have a fair coin (a coin is considered fair if there is an equal probability of being heads or tails after a flip). In other words, each coin flip i follows an independent Bernoulli distribution X Ber(1/2). Define the random variable X, as: i if coin flip i results in heads 10 if coin flip i results in tails a. Suppose you flip the coin n = 10 times. Define the number of heads you observe...
ppsMDb Youlube M Inbox- navee Question 1 6 marks he points A(a,b) and C(c,d) are the opposite vertices of square ABCD in the Cartesian plane What are the coordinates of the other two vertices? Be sure to cover all cases of where A and C could bel (a) 4 marks (b) What is the area of the square ABCD? 2 marks P A(ab) (Hint: you may find the following construction useful. Calculate both p+q and p-q) C(c,d) g Minh Pham...
Midwestern Hardware must decide how many snow shovels to order for the coming snow season. Each shovel costs $15.00 and is sold for $29.95. No inventory is carried from one snow season to the next. Shovels unsold after February are sold at a discount price of $10.00. Past data indicate that sales are highly dependent on the severity of the winter season. Past seasons have been classified as mild or harsh, and the following distribution of regular price demand has...